The Incredible Shrinking Atom: The trick is to take the electron in a hydrogen atom and replace it with a muon.

The Incredible Shrinking Atom: The trick is to take the electron in a hydrogen atom and replace it with a muon.  This is a particle 207 times heavier than an electron, but otherwise very similar.  Unfortunately a muon has a half-life of just 2 microseconds: then it decays into an electron and some other crud.  

Originally shared by John Baez

Miniature atoms

In The Incredible Shrinking Man, a guy exposed to radiation becomes smaller and smaller.   Eventually he realizes he’ll shrink forever – even down to subatomic size.  Of course that’s impossible.  But guess what: we can now make miniature atoms!

In fact we can make atoms almost like hydrogen, but 1/186 times as big across.  Unfortunately they only last 2 microseconds.  But that’s still long enough for them to form molecules, and for us to do chemical experiments with them.  Chemists have gotten really good at this stuff.

The trick is to take the electron in a hydrogen atom and replace it with a muon.  This is a particle 207 times heavier than an electron, but otherwise very similar.  Unfortunately a muon has a half-life of just 2 microseconds: then it decays into an electron and some other crud.  

Why is an ordinary hydrogen atom the size it is, anyway?  It’s the uncertainty principle.  The atom is making its energy as small as possible while remaining consistent with the uncertainty principle.  

A hydrogen atom is made of an electron and a proton.  If it were bigger, its potential energy would increase, because the electron would be further from the proton.  So, the atom “wants to be small”.  And without quantum mechanics to save it, it would collapse down to a point: The Incredible Shrinking Atom.

But if the atom were smaller, you’d know the position of its particles more precisely – so the uncertainty principle says you’d know their momentum less precisely.  They’d be wiggling around more wildly and unpredictably  So the kinetic energy would, on average, be higher.  

So there’s a tradeoff!  Too big means lots of potential energy.  Too small means lots of kinetic energy.  Somewhere in the middle is the best – and you can use this to actually calculate how big a hydrogen atom is!   

But what if you could change the mass of the electron?  This would change the calculation.  It turns out that making electrons heavier would make atoms smaller!  

While we can’t make electrons heavier, we can do the next best thing: use muons.

Muonic hydrogen is a muon orbiting a proton.  It’s like an atom, but much smaller than usual, so it does weirdly different things when it meets an ordinary atom.  It’s a whole new exotic playground for chemists.  

And, you can do nuclear fusion more easily if you start with smaller atoms!  It’s called muon-catalyzed fusion, and people have really done it.  The only problem is that it takes a whole lot of energy to make muons, and they don’t last long.  So, it’s not practical – it doesn’t pay off.  At least not yet.  Maybe we just need a few more brilliant ideas:

https://en.wikipedia.org/wiki/Muon-catalyzed_fusion

By the way: a while ago I talked about making a version of hydrogen where we keep the electron and replace the proton by a positively charged antimuon.  That’s called muonium.  Muonium is lighter than ordinary hydrogen but almost the same size, just a tiny bit bigger.  It’s chemically almost the same as hydrogen, except that it decays in 2 microseconds.  

With muonic hydrogen it’s the reverse: it’s a lot smaller, but it’s just a bit heavier.  It’s chemically very different from ordinary hydrogen.

Finally, for the übernerds:

If you do the calculation, you can show that the radius of a hydrogen-like atom is proportional to

mM/(m+M)

where m is the mass of the lighter particle and M is the mass of the heavier one.  If we say an electron has mass 1, then a muon has mass 207 and a proton has mass 1836.  You can use this formula to see that muonic hydrogen has a radius 1/186 as big as ordinary hydrogen, while muonium has a radius 1.004 times as big.  

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